The value of lim x → 0 + ⁡ x x 2 + x x x is equal to

Step-by-step solution

lim x → 0 + ⁡ x x 2 = e lim x → 0 + ⁡ x 2 ln ⁡ x = e L (say) L = lim x → 0 + ⁡ ln ⁡ x 1 x 2 = lim x → 0 + ⁡ 1 x - 2 x 3 applying L’ hospital rule = lim x → 0 + ⁡ - x 2 2 = 0 Hence, lim x → 0 + ⁡ x x 2 = e 0 = 1 Similarly, lim x → 0 + ⁡ x x = e lim x → 0 + ⁡ x ln x = e lim x → 0 + ⁡ ln x 1 x = e lim x → 0 + ⁡ 1 x - 1 x 2 = e lim x → 0 + ⁡ - x = e 0 = 1 Hence, lim x &#8